International Association
for Cryptologic Research

Linkable ring signatures are an important cryptographic primitive for anonymized applications, such as e-voting, e-cash and confidential transactions. To eliminate backdoor and overhead in trusted setup, transparent setup in the discrete logarithm or pairing settings has received considerable attention in practice. Recent advances have improved the proof sizes and verification efficiency of linkable ring signatures with transparent setup to achieve logarithmic bounds. Omniring (CCS `19) and RingCT 3.0 (FC `20) proposed linkable ring signatures in the discrete logarithm setting with logarithmic proof sizes with respect to the ring size, whereas DualDory (ESORICS `22) achieves logarithmic verifiability in the pairing setting. We make three novel contributions in this paper to improve the efficiency and soundness of logarithmic linkable ring signatures: (1) We report an attack on DualDory that breaks its linkability. (2) To eliminate such attacks, we present a new linkable ring signature scheme in the pairing setting with logarithmic verifiability. (3) We improve the verification efficiency of linkable ring signatures in the discrete logarithm setting, by a technique of reducing the number of group exponentiations for verification in Omniring by 50%. Furthermore, our technique is applicable to general inner-product relation proofs, which might be of independent interest. Finally, we empirically evaluate our schemes and compare them with the extant linkable ring signatures in concrete implementation.